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Simplifying 16x2 + -156x + -60 = 0 Reorder the terms: -60 + -156x + 16x2 = 0 Solving -60 + -156x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -39x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -39x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + -39x + 4x2 = 0 Solving -15 + -39x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -9.75x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -9.75x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -9.75x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -9.75x + x2 = 0 + 3.75 -9.75x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -9.75x + x2 = 3.75 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = 3.75 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = 3.75 + 23.765625 Combine like terms: 3.75 + 23.765625 = 27.515625 23.765625 + -9.75x + x2 = 27.515625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 27.515625 Calculate the square root of the right side: 5.245533815 Break this problem into two subproblems by setting (x + -4.875) equal to 5.245533815 and -5.245533815.Subproblem 1
x + -4.875 = 5.245533815 Simplifying x + -4.875 = 5.245533815 Reorder the terms: -4.875 + x = 5.245533815 Solving -4.875 + x = 5.245533815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 5.245533815 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 5.245533815 + 4.875 x = 5.245533815 + 4.875 Combine like terms: 5.245533815 + 4.875 = 10.120533815 x = 10.120533815 Simplifying x = 10.120533815Subproblem 2
x + -4.875 = -5.245533815 Simplifying x + -4.875 = -5.245533815 Reorder the terms: -4.875 + x = -5.245533815 Solving -4.875 + x = -5.245533815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -5.245533815 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -5.245533815 + 4.875 x = -5.245533815 + 4.875 Combine like terms: -5.245533815 + 4.875 = -0.370533815 x = -0.370533815 Simplifying x = -0.370533815Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.120533815, -0.370533815}Solution
x = {10.120533815, -0.370533815}
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